Invariants
Level: | $112$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $2 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 14 }{2}$ | ||||||
Cusps: | $14$ (of which $2$ are rational) | Cusp widths | $4^{8}\cdot8^{4}\cdot16^{2}$ | Cusp orbits | $1^{2}\cdot2^{4}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16I2 |
Level structure
$\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}41&16\\36&11\end{bmatrix}$, $\begin{bmatrix}81&96\\8&95\end{bmatrix}$, $\begin{bmatrix}89&104\\8&15\end{bmatrix}$, $\begin{bmatrix}105&24\\68&7\end{bmatrix}$, $\begin{bmatrix}111&4\\104&105\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 112.96.2.b.1 for the level structure with $-I$) |
Cyclic 112-isogeny field degree: | $32$ |
Cyclic 112-torsion field degree: | $768$ |
Full 112-torsion field degree: | $258048$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.96.0-8.c.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
112.96.0-8.c.1.3 | $112$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
112.384.5-112.c.1.8 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.c.2.10 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.g.1.7 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.g.2.10 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.j.1.6 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.j.2.10 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.l.1.3 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.l.2.20 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.bn.1.11 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.bn.4.22 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.bs.1.8 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.bs.2.13 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.cq.1.5 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.cq.2.14 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.cu.1.7 | $112$ | $2$ | $2$ | $5$ |
112.384.5-112.cu.2.13 | $112$ | $2$ | $2$ | $5$ |
112.384.7-112.b.1.15 | $112$ | $2$ | $2$ | $7$ |
112.384.7-112.d.1.5 | $112$ | $2$ | $2$ | $7$ |
112.384.7-112.g.1.8 | $112$ | $2$ | $2$ | $7$ |
112.384.7-112.h.1.15 | $112$ | $2$ | $2$ | $7$ |
112.384.7-112.p.1.21 | $112$ | $2$ | $2$ | $7$ |
112.384.7-112.t.1.15 | $112$ | $2$ | $2$ | $7$ |
112.384.7-112.x.1.7 | $112$ | $2$ | $2$ | $7$ |
112.384.7-112.z.1.8 | $112$ | $2$ | $2$ | $7$ |